Once an overwrapping of heat-shrink plastic material is applied to a packet of cigarettes, the packet of cigarettes is normally heated to a temperature below the melting temperature of the plastic material to heat-shrink and so better smooth the overwrapping about the packet of cigarettes. On currently marketed machines, however, heat-shrinking the overwrapping of heat-shrink plastic material involves a number of flaws, by failing to smooth the overwrapping of heat-shrink plastic material effectively over the whole surface.